Shout here for any general help on Pure Maths stuff from Y12 or Y13…
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Pure Maths128 comments to Pure Maths |
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Copyright © 2012 The Sydenham High School Mathematics Department Blog - All Rights Reserved |
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Pure MathsShout here for any general help on Pure Maths stuff from Y12 or Y13… 128 comments to Pure Maths |
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Copyright © 2012 The Sydenham High School Mathematics Department Blog - All Rights Reserved |
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Hi Rachel,
Try the vectors chapter lol! Example 31 is probably the closest.
Show that the coordinates obey the equation of the line for a specific value of the parameter:
Write the equation of the line in combined vector format and equate that to the coordinates of the point. Show that the t value which makes each line work is the same for every line.
Does that help?
JT
well i think i get the example… but if it isn’t given to me in that format-the question just gives me the position vectors of the points- then I can’t use t? Im looking at question1a from the vector questions pack you have us if that helps…
Hi Rachel,
Sorry I can’t lay my hands on the pack at the moment.
If you are given the position vectors of 2 points A and B, then find vector AB = b-a.
This will be your direction vector. Put it with one of the position vectors to get the equation of the line
eg r = a + tAB
You now have a line to work with for your third point.
Does that make sense or have I misunderstood the question? If so, type it out for me and I’ll redo it for you.
JT
I’m still confused….
The points A, B and C have position vectors 2i+j+k, 5i+7j+4k and i-j respectively, relative to a fixed origin O.
Prove that the points A, B and C lie on the straight line l.
so vector AB is 3i+6j+3k? and then i put it into r=a+tAB and I get 2+3t, 1+6t, 1+3t.
Is that correct? and I do the same for BC? But then where do I go from there?
Hi Rachel,
Sorry for the delay.
This type of question is easier than I was explaining because you can work out AC and AB and show they are multiples of the same vector, hence parallel. Then, because they both go through A, you must have the same straight line.
JT
Don’t be annoyed at me for asking a really basic question… but how to i differentiate lnx/2?
I’m trying to intergrate ln(x/2) by parts, so am I doing the right thing anyway?
Rachel
Hi Rachel,
You’re on the blog!!!!!!! How could I possibly be cross lol
Yes, you are doing the right thing. If there’s a ln term you MUST make this the one that has to be differentiated.
If you differentiate ln x you get 1/x
but if it’s a multiple of x you should use the chain rule
so if it’s ln(ax)
the derivative is a/ax which is still 1/x
ie result is still the same as if the a wasn’t there.
Problems only arise if there’s a bracket
eg ln (2x-3)
The derivative of this is 2/(2x-3) so this time the 2s won’t cancel.
Hope that helps
JT
ok so i still just get 1/x if i differentiate it? And i would no matter what value is in place of the 2, because its a constant?
So i can just learn this instead of attempting to chain rule it?
Yes, but remember it only works like this for a numerical constant.
lovely, thank you!
so still differentiating logs… dx/dt of ln(t+2) will be 1/(t+2) ? because the differential of (t+2) is just 1- thats why its on the top?
Sorry i’m just trying to get it into my head.
Hi Rachel,
Yes that’s right.
And that’s why you look for that pattern of derivative/function when integrating.
JT
PS Sounds like you’re having a fun Saturday
its definitely not the best saturday I’ve ever had!
Im attempting the june 2010 paper now but im stuck on question 3. Its implicit differentiation (i think anyway) but i don’t know how to differentiate 2 to the power of x.
I hope im not ruining your weekend with my questions…
Hi Rachel,
I’m doing school exam marking and writing reports so I’m tied to the desk too
The result you want is on page 37 of C4 – learn it! (Sorry can’t do proper powers on here)
JT
hi miss, hope you’re having a nice weekend!
I’ve got a very stuck on the June 2010 paper- its question 6a.
I’m guessing I have to use an identity- double angle? But I have no idea what to do…
Hi Rachel,
Sorry for the delay – trying to locate the question paper and Edexcel wouldn’t let me in!!
Your clue is in the cos-squared/sin-squared terms at the beginning.
Use cos^2 + sin^2 = 1 to eliminate one of them
then use your cos2x (can’t do thetas!) identity which brings in the one you’ve chosen to keep.
Hope that helps.
JT
Got it got it got it! So now they both have common trig, in the form of cos2x. and it should work out to give that answer.
Thank you.
I’m back! If the integral is negative- so i want to integrate -64sint, for example, does that mean that I get rid of the negative and the limits flip? Because I almost have the answer in a prove question… Does that make sense? Its question 8c from june 2008 if thats confusing.
Hi ms T,
could you please help me with q4d from the c4 jan 09 paper? I’m not really sure how to go about it.
Hi Rachel,
Yes, flipping the limits will get rid of the – sign for you.
Answers to June 08 are in pupilshare if you need them.
Mrs T
Hi Kiran,
Have e-mailed you the link to the mark scheme and also put it in Pupilshare.
JT
Hello,
This question is regarding Mr Williams homework and I am finding it really difficult. My main problem is I don’t know how to work out the coordinates of where two lines cross like in question 4 on the mixed exercise of 4h. How do I do it?
Thank you
Hi Becky,
Solve the equations of the 2 lines simultaneously because at the crossing point, the x and y values are the same, and they lie on both lines so work in both equations.
In Q4 you have y=this and y=that so this must = that! Does that make any sense?
JT
aaah okay, i will give that a go and get back to you to let you know how I got on.
Thank you Mrs Tibble!!!! 
Hi Mrs Tibble,
I started the core maths homework today. Ex3F Q1 went fine but I’m a bit on stuck on question 2. Question 2 asks you to find out how the two simultaneous equations form another equation when x is eliminiated. I thought really long and hard on this question but I just do not know what to do.
Thanks
Hi Sarah,
Make x the subject of the first equation and put what’s on the right into a bracket.
Now replace the x in the 2nd equation with your bracket.
Multiply out, tidy up and you should have what they say.
Have fun,
Mrs T
Hey Mrs T,
i just have a few questions about the stuff we had to do over half term
for ex 5b about co-ordinate geometry for question 1n it asks work out the gradient for (p,psquared), (q,qsquared).
i left my anser as qsqaured-psqaured/q-p but then the answer says q + p. ???
then for the stats questions ex3e question bii and biii are said in the answers to be the same : 5.08
but i can’t get this answer?? does dividing and multiplying not have an effect on sd coding?
THanks,
Fran
Hi Frances,
Core question
Top is the difference of two squares so you can factorise it and then cancel a bracket
stats question
Code the data, work out the new sd then de-code. Only decode multipy and divide though.
Question asks for sd of the data not the coded data so you should be getting the same answer each time. (Bit of a boring question!!)
Have fun,
Mrs T
ohhhhhhhhh thank you
also
for this question ‘find the values of k for which kxsqaured + 8x + 5 = 0 has real roots.
How do i go about this question?
and also for co-ordinate geometry where the question, for e.g. is ‘the line joining (c,4) to (7,6) has a gradient of 3/4′ i have got to the stage 2/7-c = 3/4 but dont know the order to do net?
thanks
Hi Frances,
For real roots, “b^2 – 4ac” > or = 0
For the second one, flip both fractions over and solve
or put a bracket round the 7-c and cross multiply.
Have fun!
JT
Thank you
Hi Mrs Tibble,
I have a question about the mixed exercise 3f homework which I am still trying to complete…argg!
question 6: Find the set values of x for which (x-1)(x-4)<2(x-4)
I am really stuck on this question because I just don't know how I can get to the answer. I thought about expanding the brackets and I tried that but I am sure that that's not right.
The answer for the question is 3<x<4 and I have no idea how I can get to that answer.
Please help!
Thanks,
Sarah
Hi Sarah,
Try sketching the two graphs to get a visual idea of what is going on.
The LHS is a smiley parabola y=(x-1)(x-4)
and the RHS is a straight line y=2x-8
The inequality is ‘less than’, so you want to know where the parabola is below the line.
At the points of intersection
x^2 -5x +4 = 2x – 8
Solve the quadratic and you’ll get your x values. From the graph you can see you need to be between them to satisfy the inequality.
Hope that helps!!!!
Mrs T
Just a quick question on trigonometry, I should probably know this but how do you work out the inverse of cosecθ?
Don’t worry, I was being obtuse (pun not intended!), I’ve worked it out now
Thanks,
Katja
Hi Mrs Tibble,
I am just finishing off the work form last week and I have got a bit stuck on Ex 5B question 7 and 8…everything i have done either gets a completely different answer to what is in the back of the book or I get positive 5 for qu8. instead of negative :/ Please can you help me?
Hi Becky,
Question 7
(3f-2)/(f-7) = 4
Take bottom bracket up to join the 4: 3f-2=4(f-7)
Multiply out bracket, tidy up and solve for f.
Question 8:
2g+4 /(-g+3) = -3
Take bottom bracket up to other side, multiply out, tidy up and solve.
These questions are very similar so you are probably making the same mistake. Putting brackets round the denominator will remind you to move it as a whole because the terms aren’t multiplied. I suspect that’s what you are doing wrong.
Hope this helps. Good luck.
Mrs T
PS I forgot to ask you for your stats on Wednesday so if you have it handy can you give it to me tomorrow please. (The 3C 3D 3E questions on sd and variance) Thanks
Thank you Mrs Tibble,
I actually have no idea what I was doing, I tried using it with a bracket and without but I think I must have got muddled with the signs. Ive got it now, silly me!
As for questions 9 and 10 do you have to prove they have the same gradient to prove they are points are on the same line?
Yes of course, will give it to you tomorrow
Hi Becky,
Yes that’s right. Let’s say the points are A, B and C
Do the gradient of AB and the gradient of AC
Same slope, both going through A therefore same line.
See you in the morning.
ahhh okay thank you! Will have a go at those and yes see you tomorrow morning!
Vishali, have you posted your 6A solution? It doesn’t seem to be there?
Login details sent via school e-mail
I have just sent it
OK it’s there now. Thanks.
I NEED HELP ON 6B
Don’t woory about the part B, I will look at again tomorrow
Umm Miss, you know the stats hw, my answers jus dont seem to match the answers. I’m probably going to find you in the day tomorrow.
Hi Mrs Tibble,
I am doing the circled questions from the exam paper you set us and ive got a bit stuck on question 7.b which means i can’t complete the rest of the question. what formula am I meant to use because I’ve tried using Un=a+d(n-1) but have confused myself. Please can you help me? I also wasn’t sure what question 10a is asking?? thank you
Hi Becky,
That’s the right formula but remember n isn’t 18 because this allowance only starts on her 11th birthday, so n=1 when she’s 11.
Q10 is completing the square. Complete the square with what’s on the left, then it will have the format of what’s on the right. Match terms to get a and b values.
Have fun
Mrs T
Thank you
So wouldn’t n=8 on her eighteenth birthday? if I have N and a, how do I work out d? and what do you mean match the terms? sorry so many questions 